﻿<!DOCTYPE html>
<!--[if IE]><![endif]-->
<html>
  
  <head>
    <meta charset="utf-8">
    <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1">
    <title>Class EigenvalueDecomposition
   </title>
    <meta name="viewport" content="width=device-width">
    <meta name="title" content="Class EigenvalueDecomposition
   ">
    <meta name="generator" content="docfx 2.56.4.0">
    
    <link rel="shortcut icon" href="../favicon.ico">
    <link rel="stylesheet" href="../styles/docfx.vendor.css">
    <link rel="stylesheet" href="../styles/docfx.css">
    <link rel="stylesheet" href="../styles/main.css">
    <meta property="docfx:navrel" content="../toc.html">
    <meta property="docfx:tocrel" content="toc.html">
    
    
    
  </head>
  <body data-spy="scroll" data-target="#affix" data-offset="120">
    <div id="wrapper">
      <header>
        
        <nav id="autocollapse" class="navbar navbar-inverse ng-scope" role="navigation">
          <div class="container">
            <div class="navbar-header">
              <button type="button" class="navbar-toggle" data-toggle="collapse" data-target="#navbar">
                <span class="sr-only">Toggle navigation</span>
                <span class="icon-bar"></span>
                <span class="icon-bar"></span>
                <span class="icon-bar"></span>
              </button>
              
              <a class="navbar-brand" href="../index.html">
                <img id="logo" class="svg" src="../logo.svg" alt="">
              </a>
            </div>
            <div class="collapse navbar-collapse" id="navbar">
              <form class="navbar-form navbar-right" role="search" id="search">
                <div class="form-group">
                  <input type="text" class="form-control" id="search-query" placeholder="Search" autocomplete="off">
                </div>
              </form>
            </div>
          </div>
        </nav>
        
        <div class="subnav navbar navbar-default">
          <div class="container hide-when-search" id="breadcrumb">
            <ul class="breadcrumb">
              <li></li>
            </ul>
          </div>
        </div>
      </header>
      <div role="main" class="container body-content hide-when-search">
        
        <div class="sidenav hide-when-search">
          <a class="btn toc-toggle collapse" data-toggle="collapse" href="#sidetoggle" aria-expanded="false" aria-controls="sidetoggle">Show / Hide Table of Contents</a>
          <div class="sidetoggle collapse" id="sidetoggle">
            <div id="sidetoc"></div>
          </div>
        </div>
        <div class="article row grid-right">
          <div class="col-md-10">
            <article class="content wrap" id="_content" data-uid="CADability.LinearAlgebra.EigenvalueDecomposition">
  
  
  <h1 id="CADability_LinearAlgebra_EigenvalueDecomposition" data-uid="CADability.LinearAlgebra.EigenvalueDecomposition" class="text-break">Class EigenvalueDecomposition
  </h1>
  <div class="markdown level0 summary"><p>Eigenvalues and eigenvectors of a real matrix.</p>
</div>
  <div class="markdown level0 conceptual"></div>
  <div class="inheritance">
    <h5>Inheritance</h5>
    <div class="level0"><span class="xref">System.Object</span></div>
    <div class="level1"><span class="xref">EigenvalueDecomposition</span></div>
  </div>
  <div class="inheritedMembers">
    <h5>Inherited Members</h5>
    <div>
      <span class="xref">System.Object.Equals(System.Object)</span>
    </div>
    <div>
      <span class="xref">System.Object.Equals(System.Object, System.Object)</span>
    </div>
    <div>
      <span class="xref">System.Object.GetHashCode()</span>
    </div>
    <div>
      <span class="xref">System.Object.GetType()</span>
    </div>
    <div>
      <span class="xref">System.Object.MemberwiseClone()</span>
    </div>
    <div>
      <span class="xref">System.Object.ReferenceEquals(System.Object, System.Object)</span>
    </div>
    <div>
      <span class="xref">System.Object.ToString()</span>
    </div>
  </div>
  <h6><strong>Namespace</strong>: <a class="xref" href="CADability.LinearAlgebra.html">CADability.LinearAlgebra</a></h6>
  <h6><strong>Assembly</strong>: CADability.dll</h6>
  <h5 id="CADability_LinearAlgebra_EigenvalueDecomposition_syntax">Syntax</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">[Serializable]
public class EigenvalueDecomposition</code></pre>
  </div>
  <h5 id="CADability_LinearAlgebra_EigenvalueDecomposition_remarks"><strong>Remarks</strong></h5>
  <div class="markdown level0 remarks"><p>If A is symmetric, then A = V<em>D</em>V' where the eigenvalue matrix D is
diagonal and the eigenvector matrix V is orthogonal.
I.e. A = V.Multiply(D.Multiply(V.Transpose())) and
V.Multiply(V.Transpose()) equals the identity matrix.
If A is not symmetric, then the eigenvalue matrix D is block diagonal
with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
lambda + i<em>mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda].  The
columns of V represent the eigenvectors in the sense that A</em>V = V<em>D,
i.e. A.Multiply(V) equals V.Multiply(D).  The matrix V may be badly
conditioned, or even singular, so the validity of the equation
A = V</em>D*Inverse(V) depends upon V.cond().</p>
</div>
  <h3 id="constructors">Constructors
  </h3>
  <span class="small pull-right mobile-hide">
    <span class="divider">|</span>
    <a href="https://github.com/SOFAgh/CADability/new/NonPeriodicAndImplicitSurfaces/apiSpec/new?filename=CADability_LinearAlgebra_EigenvalueDecomposition__ctor_CADability_LinearAlgebra_Matrix_.md&amp;value=---%0Auid%3A%20CADability.LinearAlgebra.EigenvalueDecomposition.%23ctor(CADability.LinearAlgebra.Matrix)%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
  </span>
  <span class="small pull-right mobile-hide">
    <a href="https://github.com/SOFAgh/CADability/blob/NonPeriodicAndImplicitSurfaces/CADability/EigenvalueDecomposition.cs/#L1012">View Source</a>
  </span>
  <a id="CADability_LinearAlgebra_EigenvalueDecomposition__ctor_" data-uid="CADability.LinearAlgebra.EigenvalueDecomposition.#ctor*"></a>
  <h4 id="CADability_LinearAlgebra_EigenvalueDecomposition__ctor_CADability_LinearAlgebra_Matrix_" data-uid="CADability.LinearAlgebra.EigenvalueDecomposition.#ctor(CADability.LinearAlgebra.Matrix)">EigenvalueDecomposition(Matrix)</h4>
  <div class="markdown level1 summary"><p>Check for symmetry, then construct the eigenvalue decomposition</p>
</div>
  <div class="markdown level1 conceptual"></div>
  <h5 class="decalaration">Declaration</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">public EigenvalueDecomposition(Matrix Arg)</code></pre>
  </div>
  <h5 class="parameters">Parameters</h5>
  <table class="table table-bordered table-striped table-condensed">
    <thead>
      <tr>
        <th>Type</th>
        <th>Name</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td><a class="xref" href="CADability.LinearAlgebra.Matrix.html">Matrix</a></td>
        <td><span class="parametername">Arg</span></td>
        <td><p>Square matrix</p>
</td>
      </tr>
    </tbody>
  </table>
  <h5 id="CADability_LinearAlgebra_EigenvalueDecomposition__ctor_CADability_LinearAlgebra_Matrix__remarks">Remarks</h5>
  <div class="markdown level1 remarks"><p>Provides access to D and V</p>
</div>
  <span class="small pull-right mobile-hide">
    <span class="divider">|</span>
    <a href="https://github.com/SOFAgh/CADability/new/NonPeriodicAndImplicitSurfaces/apiSpec/new?filename=CADability_LinearAlgebra_EigenvalueDecomposition__ctor_System_Double___System_Double___.md&amp;value=---%0Auid%3A%20CADability.LinearAlgebra.EigenvalueDecomposition.%23ctor(System.Double%5B%5D%2CSystem.Double%5B%5D)%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
  </span>
  <span class="small pull-right mobile-hide">
    <a href="https://github.com/SOFAgh/CADability/blob/NonPeriodicAndImplicitSurfaces/CADability/EigenvalueDecomposition.cs/#L1068">View Source</a>
  </span>
  <a id="CADability_LinearAlgebra_EigenvalueDecomposition__ctor_" data-uid="CADability.LinearAlgebra.EigenvalueDecomposition.#ctor*"></a>
  <h4 id="CADability_LinearAlgebra_EigenvalueDecomposition__ctor_System_Double___System_Double___" data-uid="CADability.LinearAlgebra.EigenvalueDecomposition.#ctor(System.Double[],System.Double[])">EigenvalueDecomposition(Double[], Double[])</h4>
  <div class="markdown level1 summary"><p>Constructs the eigenvalue decomposition from a symmetrical,
tridiagonal matrix.</p>
</div>
  <div class="markdown level1 conceptual"></div>
  <h5 class="decalaration">Declaration</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">public EigenvalueDecomposition(double[] d, double[] e)</code></pre>
  </div>
  <h5 class="parameters">Parameters</h5>
  <table class="table table-bordered table-striped table-condensed">
    <thead>
      <tr>
        <th>Type</th>
        <th>Name</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td><span class="xref">System.Double</span>[]</td>
        <td><span class="parametername">d</span></td>
        <td></td>
      </tr>
      <tr>
        <td><span class="xref">System.Double</span>[]</td>
        <td><span class="parametername">e</span></td>
        <td></td>
      </tr>
    </tbody>
  </table>
  <h3 id="properties">Properties
  </h3>
  <span class="small pull-right mobile-hide">
    <span class="divider">|</span>
    <a href="https://github.com/SOFAgh/CADability/new/NonPeriodicAndImplicitSurfaces/apiSpec/new?filename=CADability_LinearAlgebra_EigenvalueDecomposition_BlockDiagonal.md&amp;value=---%0Auid%3A%20CADability.LinearAlgebra.EigenvalueDecomposition.BlockDiagonal%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
  </span>
  <span class="small pull-right mobile-hide">
    <a href="https://github.com/SOFAgh/CADability/blob/NonPeriodicAndImplicitSurfaces/CADability/EigenvalueDecomposition.cs/#L1113">View Source</a>
  </span>
  <a id="CADability_LinearAlgebra_EigenvalueDecomposition_BlockDiagonal_" data-uid="CADability.LinearAlgebra.EigenvalueDecomposition.BlockDiagonal*"></a>
  <h4 id="CADability_LinearAlgebra_EigenvalueDecomposition_BlockDiagonal" data-uid="CADability.LinearAlgebra.EigenvalueDecomposition.BlockDiagonal">BlockDiagonal</h4>
  <div class="markdown level1 summary"><p>Gets the block diagonal eigenvalue matrix</p>
</div>
  <div class="markdown level1 conceptual"></div>
  <h5 class="decalaration">Declaration</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">public Matrix BlockDiagonal { get; }</code></pre>
  </div>
  <h5 class="propertyValue">Property Value</h5>
  <table class="table table-bordered table-striped table-condensed">
    <thead>
      <tr>
        <th>Type</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td><a class="xref" href="CADability.LinearAlgebra.Matrix.html">Matrix</a></td>
        <td></td>
      </tr>
    </tbody>
  </table>
  <span class="small pull-right mobile-hide">
    <span class="divider">|</span>
    <a href="https://github.com/SOFAgh/CADability/new/NonPeriodicAndImplicitSurfaces/apiSpec/new?filename=CADability_LinearAlgebra_EigenvalueDecomposition_EigenValues.md&amp;value=---%0Auid%3A%20CADability.LinearAlgebra.EigenvalueDecomposition.EigenValues%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
  </span>
  <span class="small pull-right mobile-hide">
    <a href="https://github.com/SOFAgh/CADability/blob/NonPeriodicAndImplicitSurfaces/CADability/EigenvalueDecomposition.cs/#L1095">View Source</a>
  </span>
  <a id="CADability_LinearAlgebra_EigenvalueDecomposition_EigenValues_" data-uid="CADability.LinearAlgebra.EigenvalueDecomposition.EigenValues*"></a>
  <h4 id="CADability_LinearAlgebra_EigenvalueDecomposition_EigenValues" data-uid="CADability.LinearAlgebra.EigenvalueDecomposition.EigenValues">EigenValues</h4>
  <div class="markdown level1 summary"><p>Gets the eigenvalues.</p>
</div>
  <div class="markdown level1 conceptual"></div>
  <h5 class="decalaration">Declaration</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">public Complex[] EigenValues { get; }</code></pre>
  </div>
  <h5 class="propertyValue">Property Value</h5>
  <table class="table table-bordered table-striped table-condensed">
    <thead>
      <tr>
        <th>Type</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td><a class="xref" href="MathNet.Numerics.Complex.html">Complex</a>[]</td>
        <td><p>diag(D)</p>
</td>
      </tr>
    </tbody>
  </table>
  <span class="small pull-right mobile-hide">
    <span class="divider">|</span>
    <a href="https://github.com/SOFAgh/CADability/new/NonPeriodicAndImplicitSurfaces/apiSpec/new?filename=CADability_LinearAlgebra_EigenvalueDecomposition_EigenVectors.md&amp;value=---%0Auid%3A%20CADability.LinearAlgebra.EigenvalueDecomposition.EigenVectors%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
  </span>
  <span class="small pull-right mobile-hide">
    <a href="https://github.com/SOFAgh/CADability/blob/NonPeriodicAndImplicitSurfaces/CADability/EigenvalueDecomposition.cs/#L1143">View Source</a>
  </span>
  <a id="CADability_LinearAlgebra_EigenvalueDecomposition_EigenVectors_" data-uid="CADability.LinearAlgebra.EigenvalueDecomposition.EigenVectors*"></a>
  <h4 id="CADability_LinearAlgebra_EigenvalueDecomposition_EigenVectors" data-uid="CADability.LinearAlgebra.EigenvalueDecomposition.EigenVectors">EigenVectors</h4>
  <div class="markdown level1 summary"><p>Returns the eigenvector matrix</p>
</div>
  <div class="markdown level1 conceptual"></div>
  <h5 class="decalaration">Declaration</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">public Matrix EigenVectors { get; }</code></pre>
  </div>
  <h5 class="propertyValue">Property Value</h5>
  <table class="table table-bordered table-striped table-condensed">
    <thead>
      <tr>
        <th>Type</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td><a class="xref" href="CADability.LinearAlgebra.Matrix.html">Matrix</a></td>
        <td></td>
      </tr>
    </tbody>
  </table>
  <span class="small pull-right mobile-hide">
    <span class="divider">|</span>
    <a href="https://github.com/SOFAgh/CADability/new/NonPeriodicAndImplicitSurfaces/apiSpec/new?filename=CADability_LinearAlgebra_EigenvalueDecomposition_ImagEigenvalues.md&amp;value=---%0Auid%3A%20CADability.LinearAlgebra.EigenvalueDecomposition.ImagEigenvalues%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
  </span>
  <span class="small pull-right mobile-hide">
    <a href="https://github.com/SOFAgh/CADability/blob/NonPeriodicAndImplicitSurfaces/CADability/EigenvalueDecomposition.cs/#L1108">View Source</a>
  </span>
  <a id="CADability_LinearAlgebra_EigenvalueDecomposition_ImagEigenvalues_" data-uid="CADability.LinearAlgebra.EigenvalueDecomposition.ImagEigenvalues*"></a>
  <h4 id="CADability_LinearAlgebra_EigenvalueDecomposition_ImagEigenvalues" data-uid="CADability.LinearAlgebra.EigenvalueDecomposition.ImagEigenvalues">ImagEigenvalues</h4>
  <div class="markdown level1 summary"><p>Gets the imaginary part of the eigenvalues</p>
</div>
  <div class="markdown level1 conceptual"></div>
  <h5 class="decalaration">Declaration</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">public double[] ImagEigenvalues { get; }</code></pre>
  </div>
  <h5 class="propertyValue">Property Value</h5>
  <table class="table table-bordered table-striped table-condensed">
    <thead>
      <tr>
        <th>Type</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td><span class="xref">System.Double</span>[]</td>
        <td><p>imag(diag(D))</p>
</td>
      </tr>
    </tbody>
  </table>
  <span class="small pull-right mobile-hide">
    <span class="divider">|</span>
    <a href="https://github.com/SOFAgh/CADability/new/NonPeriodicAndImplicitSurfaces/apiSpec/new?filename=CADability_LinearAlgebra_EigenvalueDecomposition_RealEigenvalues.md&amp;value=---%0Auid%3A%20CADability.LinearAlgebra.EigenvalueDecomposition.RealEigenvalues%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
  </span>
  <span class="small pull-right mobile-hide">
    <a href="https://github.com/SOFAgh/CADability/blob/NonPeriodicAndImplicitSurfaces/CADability/EigenvalueDecomposition.cs/#L1102">View Source</a>
  </span>
  <a id="CADability_LinearAlgebra_EigenvalueDecomposition_RealEigenvalues_" data-uid="CADability.LinearAlgebra.EigenvalueDecomposition.RealEigenvalues*"></a>
  <h4 id="CADability_LinearAlgebra_EigenvalueDecomposition_RealEigenvalues" data-uid="CADability.LinearAlgebra.EigenvalueDecomposition.RealEigenvalues">RealEigenvalues</h4>
  <div class="markdown level1 summary"><p>Gets the real part of the eigenvalues.</p>
</div>
  <div class="markdown level1 conceptual"></div>
  <h5 class="decalaration">Declaration</h5>
  <div class="codewrapper">
    <pre><code class="lang-csharp hljs">public double[] RealEigenvalues { get; }</code></pre>
  </div>
  <h5 class="propertyValue">Property Value</h5>
  <table class="table table-bordered table-striped table-condensed">
    <thead>
      <tr>
        <th>Type</th>
        <th>Description</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td><span class="xref">System.Double</span>[]</td>
        <td><p>real(diag(D))</p>
</td>
      </tr>
    </tbody>
  </table>
</article>
          </div>
          
          <div class="hidden-sm col-md-2" role="complementary">
            <div class="sideaffix">
              <div class="contribution">
                <ul class="nav">
                  <li>
                    <a href="https://github.com/SOFAgh/CADability/new/NonPeriodicAndImplicitSurfaces/apiSpec/new?filename=CADability_LinearAlgebra_EigenvalueDecomposition.md&amp;value=---%0Auid%3A%20CADability.LinearAlgebra.EigenvalueDecomposition%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A" class="contribution-link">Improve this Doc</a>
                  </li>
                  <li>
                    <a href="https://github.com/SOFAgh/CADability/blob/NonPeriodicAndImplicitSurfaces/CADability/EigenvalueDecomposition.cs/#L44" class="contribution-link">View Source</a>
                  </li>
                </ul>
              </div>
              <nav class="bs-docs-sidebar hidden-print hidden-xs hidden-sm affix" id="affix">
                <h5>In This Article</h5>
                <div></div>
              </nav>
            </div>
          </div>
        </div>
      </div>
      
      <footer>
        <div class="grad-bottom"></div>
        <div class="footer">
          <div class="container">
            <span class="pull-right">
              <a href="#top">Back to top</a>
            </span>
            
            <span>Generated by <strong>DocFX</strong></span>
          </div>
        </div>
      </footer>
    </div>
    
    <script type="text/javascript" src="../styles/docfx.vendor.js"></script>
    <script type="text/javascript" src="../styles/docfx.js"></script>
    <script type="text/javascript" src="../styles/main.js"></script>
  </body>
</html>
